The Bulldogs (9-2 overall, 7-1 Southeastern Conference) leaned on Walsh's four field goals, including three from 39 yards, and strong defense to clinch first place in the SEC's Eastern Division.
Georgia fans chanted ''SEC! SEC'' with less than 1 minute remaining as players emptied a cooler on coach Mark Richt.
Georgia will play in the SEC championship game for the fourth time in 11 seasons under Richt. It won SEC titles under Richt in 2002 and in 2005, its last appearance in the game.
The loss eliminated the Wildcats, who have appeared in a school-record five straight bowl games, from postseason consideration.
Georgia went into the half ahead 12-10 on Walsh's four field goals before finally reaching the end zone as the fourth quarter started. On third down from the Kentucky 7, Murray stepped up and passed to Brown in the back of the end zone.
Murray completed 16 of 29 passes for 162 yards with one touchdown and one interception.
Kentucky's Smith completed 17 of 35 passes for 133 yards with one touchdown, two interceptions and a fumble.
Crowell, a freshman who began the day with 821 yards rushing, ran straight ahead for 6 yards on his first carry and then limped off the field with the left ankle injury after running for 5 yards on his second carry. The freshman limped to the locker room later in the first quarter and returned but remained on the sideline, standing unsteadily on his sore ankle.
He had only a sock on his left foot as he sat and watched in the second half.
Crowell's status for Georgia's final regular-season game at Georgia Tech next week is uncertain.
Harton and Malcome each lost fumbles. Harton had only 12 yards rushing in the first half before finishing with 101.
Georgia announced before the game Thomas was not at the game and was not suspended. Crowell, Thomas and Malcome were suspended for one game earlier in the season.
Kentucky moved 65 yards on its first possession and took a 3-0 lead on Craig McIntosh's 32-yard field goal. It was a promising start to what proved to be a disappointing day for Kentucky's offense against Georgia, which ranks fourth in the nation in total defense.
The Wildcats were held without a first down in the second half until there were about 3 minutes remaining in the game.